Industrial control systems are used to control a wide variety of industrial processes. Examples of such processes include the control of steel rolling mills (to maintain uniform output thickness of rolled steel strip), ship stabilization, dynamic ship positioning, adaptive ship autopilots, temperature control of buildings, radio aerial tracking, and a wide variety of chemical processes.
In all such processes, the problem in general terms is to maintain a desired quantity (such as the heading of a ship) constant (or following a desired pattern) in the face of peculiarities of the apparatus itself (such as slow response time of the rudder in turning to a desired position, and of the ship in turning in response to a rudder position change) and external influences (such as steady cross currents and varying wind forces). The control system (controller, actuators, and sensors) measures the desired quantity and generates a control signal which is fed into the system being controlled (as a control signal to the rudder position gear).
The controller can be regarded, in mathematical terms, as calculating the control signal as some function of the measured quantity. The particular function chosen can generally be regarded as a transfer function having a particular form (e.g. a polynomial of given degree) and having particular parameters (which would then be the coefficients of the various terms of the polynomial). The form of the function is chosen from a knowledge of the general characteristics of the system to be controlled. The parameters of the chosen form can then be determined in various ways, involving measurement or calculation of the characteristics of the system to be controlled.
In many control systems, the controller parameters are fully defined by the initial design, and the controller provides satisfactory control. However, in some systems, the operating conditions and/or system characteristics vary widely with time; for example, the characteristics of a cargo ship will differ widely depending on its speed, whether it is fully laden or in ballast, etc. In such circumstances, it may be desirable for the control system to be adaptive. For that, the characteristics of the system are monitored and the parameters of the controller are adjusted accordingly. Thus the control system does not merely calculate the control signal in dependence on the measured quantity; it also adapts itself to changes which are detected in the general characteristics or behaviour of the system being controlled by continual parameter adjustment.
One known controller design technique is known as H.infin. (H-infinity) design. This has various advantages, but it has the drawback that the calculations involved in determining an H.infin. controller in any particular instance are in general very complicated and involved. The H.infin. method has therefore generally been used for the initial (off-line) design of controllers.